It sounds to me like the Rated Power has been specified in RMS, and the derivation of Music Power is directly as a result of so many manufacturers rating systems by the peak-to-peak measurement of the rated output. Fostex are just trying not to get left behind in the rush of exaggerated power output advertising blurb.

I found my answer, I though I would share. It was on the Fostexinternational website.

INPUT POWER
Indication of input power may be for both 'maximum allowable input power' and 'rated input power', or for either one of them. The fact that they are given different definitions makes it necessary to confirm that such figures are adequate for your intended application.

(1) MAXIMUM ALLOWABLE INPUT POWER
This term defines the maximum input power which can be momentarily applied to the driver. However, note must be taken that such power is a measurement of certain individual frequencies, and thus, not allowed for every frequency point. To be safe, input power defined using the term 'Music' should be considered, in that it indicates peak input power encountered during reproduction of a general music source. In no sense do input values mean that no sound will be produced unless such power is input, nor may drivers be damaged unless the output power of an amplifier is lower than the input value. Under ordinary listening conditions in homes, the possibility of excessive power being input will be rare even with an amplifier having output capability of up to several hundred watts, except under extraordinary conditions. Apart from occasions for PA purposes or where drivers are driven for experimental purposes, input values may be regarded as certain guidelines for enjoyable reproduction of Hi-Fi sound in homes.

(2) RATED INPUT POWER
This value represents the upper limit of the power which may be continuously input into drivers. It must be noted, however, that, as with the maximum allowable input power, such values are effective only for certain selected frequencies, not for the entire audio spectrum. Nor, does it mean that such value can be input if the frequency of interest is constant, as for some special purposes such as measurement or experiment purposes. Continuous input of a single frequency should be interpreted as if the driver load is substantial and very burdensome.